Numerical Simulations of the ISM: What Good are They?

Transcription

1 Numerical Simulations of the ISM: What Good are They? Alyssa A. Goodman Harvard-Smithsonian Center for Astrophysics Principal Collaborators Héctor Arce, CfA Javier Ballesteros-Paredes, AMNH Sungeun Kim, CfA Paolo Padoan, CfA Erik Rosolowsky, UC Berkeley Enrique Vazquez-Semadeni, UNAM Jonathan Williams, U. Florida David Wilner, CfA

2 Spectroscopy Velocity Information Observed Spectrum Telescope + Spectrometer Intensity "Velocity"

3 Radio Spectral-line Observations of Interstellar Clouds Spectral Line Observations

4 The Superstore: Learning More from Too Much Data Product (S/N)*N pixels *N channels N channels S/N N pixels N channels, S/N in 1 hour, N pixels Year

5 A Free Sample Data: Hartmann & Burton 1999; Figure: Ballesteros-Paredes, Vazquez-Semadeni & Goodman 2001

6 The Good Old Days Low Observational Resolution Models of spherical, Smooth, Long-lasting Cloud Structures And more structure came from fragmentation

7 The New Age High(er) Observational Resolution (at many λ s) Highly irregular structures, many of which are transient on long time scales

8 So, are numerical simulations physically illuminating in this New Age? If so, in what way(s)? How might simulations be improved (i.e. to better match observations)?

9 Numerical MHD: The State of the Art 25 Years Ago Two-dimensional CEL code 10 s of hours of CPU time Only possible to run 1 case Grid size ~96 x 188 (~128 2 ) No magnetic fields No gravity Heating & cooling treated R-T and K-H Instabilities traced well Star-formation triggered by a spiraldensity wave shock. (Woodward 1976)

10 Woodward s Conclusions (1976)

11 Y2K MHD β=0.01 β=1 Stone, Gammie & Ostriker 1999 β [ T /10 K] = [ nh 2 /100 cm -3 ][ B /1.4 µg] 2 Driven Turbulence; M K; no gravity Colors: log density Computational volume: Dark blue lines: B-field Red : isosurface of passive contaminant after saturation

12 But, recall what we actually observe Intensity(position, position,velocity) Falgarone et al. 1994

13 Velocity is the Observer s "Fourth" Dimension Spectral Line Observations Loss of 1 dimension Mountain Range No loss of information

14 Statistical Tools Can no longer examine large spectral-line maps or simulations by-eye Need powerful, discriminatory tools to quantify and intercompare data sets Previous attempts are numerous: ACF, Structure Functions, Structure Trees, Clumpfinding, Wavelets, PCA, -variance, Line parameter histograms Most previous attempts discard or compress either position or velocity information

15 1997 Goals of the Spectral Correlation Function Project Develop sharp tool for statistical analysis of ISM, using as much data of a data cube as possible! Compare information from this tool with other statistical tools applied to same cubes Incorporate continuum information! Use best suite of tools to compare real & simulated ISM! Adjust simulations to match, understanding physical inputs! Develop a (better) prescription for finding star-forming gas

16 The Spectral Correlation Function v.1.0 Simply measures similarity of neighboring spectra (Rosolowsky, Goodman, Wilner & Williams 1999) S/N equalized, observational/theoretical comparisons show discriminatory power After explaining v.1.0, I ll show: v.2.0 Measures spectral similarity as a function of spatial scale Applications

17 How SCF v.1.0 Works Measures similarity of neighboring spectra within a specified beam size lag & scaling adjustable signal-to-noise accounted for See: Rosolowsky, Goodman, Wilner & Williams 1999; Ballesteros-Paredes, Vazquez-Semadeni & Goodman 2001

18 Antenna Temperature Map greyscale: T A =0.04 to 0. 3 K Raw SCF Map Application of the Raw SCF greyscale: while=low correlation; black=high Data shown: C 18 O map of Rosette, courtesy M. Heyer et al. Results: Padoan, Rosolowsky & Goodman 2001

19 Antenna Temperature Map greyscale: T A =0.04 to 0. 3 K Normalized SCF Map Application of the SCF greyscale: while=low correlation; black=high Data shown: C 18 O map of Rosette, courtesy M. Heyer et al. Results: Padoan, Rosolowsky & Goodman 2001.

20 Randomized Positions Original Data SCF Distributions Normalized C 18 O Data for Rosette Molecular Cloud

21 Unbound High-Latitude Cloud Self-Gravitating, Star-Forming Region Insights from SCF v.1.0 Rosolowsky, Goodman, Williams & Wilner 1999 Lag & scaling adjustable Only lag adjustable Only scaling adjustable No adjustments Observations Simulations No gravity, No B field No gravity, Yes B field Yes gravity, Yes B field

22 Which of these is not like the others? Change in Mean SCF with Randomization Increasing Similarity of Spectra to Neighbors SNR H I Survey Rosette C 18 O Peaks G,O,S L134A 12 CO(2-1). MacLow et al. Rosette C 18 O Rosette 13 CO Rosette 13 CO Peaks HCl2 C 18 O L134A 13 CO(1-0) Pol. 13 CO(1-0) L CO(2-1) HCl2 C 18 O Peaks HLC Increasing Similarity of ALL Spectra in Map Falgarone et al Mean SCF Value

23 The Spectral Correlation Function v.1.0 Simply measures similarity of neighboring spectra (Rosolowsky, Goodman, Wilner & Williams 1999) S/N equalized, observational/theoretical comparisons show discriminatory power v.2.0 Measures spectral similarity as a function of spatial scale (Padoan, Rosolowsky & Goodman 2001) Noise normalization technique found SCF(lag) even more powerful discriminant Applications Finding the scale-height of face-on galaxies! (Padoan, Kim, Goodman & Stavely-Smith 2001) Understanding behavior of atomic ISM (e.g. Ballesteros-Paredes, Vazquez-Semadeni & Goodman 2001)

24 v.2.0: Scale-Dependence of the SCF Example for Simulated Data Padoan, Rosolowsky & Goodman 2001

25 A Robust Statistic High-resolution data Low-resolution data, area of high-res map Low-resolution data, full map Padoan, Rosolowsky & Goodman 2001

26 The Spectral Correlation Function v.1.0 Simply measures similarity of neighboring spectra (Rosolowsky, Goodman, Wilner & Williams 1999) S/N equalized, observational/theoretical comparisons show discriminatory power v.2.0 Measures spectral similarity as a function of spatial scale (Padoan, Rosolowsky & Goodman 2001) Noise normalization technique found SCF(lag) even more powerful discriminant Applications Finding the scale-height of face-on galaxies! (Padoan, Kim, Goodman & Stavely-Smith 2001) Understanding behavior of atomic ISM (e.g. Ballesteros-Paredes, Vazquez-Semadeni & Goodman 2001)

27 Galactic Scale Heights from the SCF (v.2.0) HI map of the LMC from ATCA & Parkes Multi-Beam, courtesy Stavely-Smith, Kim, et al. Padoan, Kim, Goodman & Stavely-Smith 2001

28 The Behavior of the Atomic ISM Data: Hartmann & Burton 1999; Figure: Ballesteros-Paredes, Vazquez-Semadeni & Goodman 2001

29 Insights into Atomic ISM from SCF (v.1.0) Comparison with simulations of Vazquez-Semadeni & collaborators shows: Thermal Broadening of H I Line Profiles can hide much of the true velocity structure SCF v.1.0 good at picking out shock-like structure in H I maps (also gives low correlation tail) See Ballesteros-Paredes, Vazquez-Semadeni & Goodman 2001.

30 Revealing Shortcomings of a Simulation Thermally Broadened, very high T Velocity histogram, 16 bins Velocity histogram, 64 bins Ballesteros-Paredes, Vazquez-Semadeni & Goodman 2001

31 Insights into Atomic ISM from SCF (v.1.0) From v-histograms, 64 bins

32 Insights into Atomic ISM from SCF (v.1.0) Thermally Broadened, very high T

33 Insights into Atomic ISM from SCF (v.1.0) Thermally Broadened, equivalent of much lower T--best match!

34 A Success of the SCF Sample spectra after velocity scale expanded x6 (to mimic lower temperature, and give more importance to turbulence in determining line shape) Ballesteros-Paredes, Vazquez-Semadeni & Goodman 2001

35 The Spectral Correlation Function v.1.0 Simply measures similarity of neighboring spectra (Rosolowsky, Goodman, Wilner & Williams 1999) S/N equalized, observational/theoretical comparisons show discriminatory power v.2.0 Measures spectral similarity as a function of spatial scale (Padoan, Rosolowsky & Goodman 2001) Noise normalization technique found SCF(lag) even more powerful discriminant Applications Finding the scale-height of face-on galaxies! (Padoan, Kim, Goodman & Stavely-Smith 2001) Understanding behavior of atomic ISM (e.g. Ballesteros-Paredes, Vazquez-Semadeni & Goodman 2001)

36 How about applying the SCF to the ionized ISM? WHAM Results from Haffner, Reynolds & Tufte 1999

37 What good are they anyway?? (In case you re still not convinced:) MHD Simulations illumination of observed emission polarization maps MHD Simulations & the IMF (ask me later)

38 SCUBA Polarimetry of Dense Cores & Globules Polarization drops with submm flux (similar to p decreasing with A V ) Does polarization map give true field structure? Plots and data from Henning, Wolf, Launhart & Waters 2001

39 Simulated Polarized Emission 3-D simulation super-sonic super-alfvénic self-gravitating Model A: Uniform grainalignment efficiency C2 C3 C1 Padoan, Goodman, Draine, Juvela,Nordlund, Rögnvaldsson 2001

40 Simulated Polarized Emission 3-D simulation super-sonic super-alfvénic self-gravitating Model B: Poor Alignment at A V 3 mag C2 A V,0 =3 mag C3 C1 Padoan, Goodman, Draine, Juvela,Nordlund, Rögnvaldsson 2001

41 SCUBA-like Cores Core C1 Core C2 Core C3 Core C1; A V,0 =3 mag Core C2; A V,0 =3 mag Core C3; A V,0 =3 mag Padoan, Goodman, Draine, Juvela,Nordlund, Rögnvaldsson 2001

42 Core C1y 10 8 Core C1y (A V,0 =3 mag) Polarization vs. Intensity I/I max Core C2y I/I max I/I max Core C3y I/I max Core C2y (A V,0 =3 mag) I/I max I/I max Core C3y (A V,0 =3 mag) Padoan, Goodman, Draine, Juvela,Nordlund, Rögnvaldsson 2001

43 The Meaning of a Clump IMF, c What is a clump? +=dense core Typical Stellar IMF dn dm M 2.5±0.3 Salpeter 1955 Miller & Scalo 1979 Structure-Finding Algorithms What does the clump IMF look like? y dn dm M 16. v x CS (2 1) E. Lada 1992 E. Lada et al CLUMPFIND (Williams et al. 1994) Autocorrelations (e.g. Miesch & Bally 1994) Structure Trees (Houlahan & Scalo 1990,92) GAUSSCLUMPS (Stutzki & Güesten 1990) Wavelets (e.g. Langer et al. 1993) Complexity (Wiseman & Adams 1994) IR Star-Counting (C. Lada et al. 1994)

44 Simulating the IMF--in the Gas: Success? Includes ONLY: Simulated clumps massive enough to collapse and form a star Padoan, Nordlund, Rognvaldsson & Goodman 2001; see also Klessen 2001

45 Acheivements & Plans Acheievements SCF most discriminating descriptor of spectralline data cubes SCF used to map scale height in the LMC SCF used to revise/improve MHD simulations Plans Use the SCF to find star-forming gas observationally Try the SCF on the ionized ISM Study galaxy structure with SCF applied to extragalactic CO (BIMA SONG; ALMA) and H I (EVLA; SKA) maps